Height on Side B of Triangle Calculator

Formula Used:

\[ h_b = \frac{\sqrt{(S_a + S_b + S_c) \times (S_b - S_a + S_c) \times (S_a - S_b + S_c) \times (S_a + S_b - S_c)}}{2 \times S_b} \]

Height on Side B of Triangle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Height on Side B of Triangle?

The Height on Side B of a Triangle is the length of the perpendicular drawn from the vertex opposite to side B to side B itself. It represents the shortest distance from that vertex to side B.

2. How Does the Calculator Work?

The calculator uses the following formula derived from Heron's formula:

\[ h_b = \frac{\sqrt{(S_a + S_b + S_c) \times (S_b - S_a + S_c) \times (S_a - S_b + S_c) \times (S_a + S_b - S_c)}}{2 \times S_b} \]

Where:

\( h_b \) — Height on Side B of Triangle (m)
\( S_a \) — Side A of Triangle (m)
\( S_b \) — Side B of Triangle (m)
\( S_c \) — Side C of Triangle (m)

Explanation: This formula calculates the height on side B using all three sides of the triangle, based on the area calculation from Heron's formula.

3. Importance of Height Calculation

Details: Calculating heights in triangles is essential for various geometric calculations, construction projects, engineering designs, and trigonometric applications. It helps determine the area of triangles and solve complex geometric problems.

4. Using the Calculator

Tips: Enter all three side lengths in meters. Ensure the values satisfy the triangle inequality theorem (sum of any two sides must be greater than the third side). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the triangle inequality theorem?
A: The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Q2: Can this formula be used for all types of triangles?
A: Yes, this formula works for all types of triangles - acute, obtuse, and right triangles, as long as the side lengths satisfy the triangle inequality.

Q3: What units should I use for the inputs?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as long as all three sides are in the same unit.

Q4: Why does the calculator show an error message?
A: The calculator shows an error if the input values don't form a valid triangle (violate triangle inequality) or if any side length is zero or negative.

Q5: How accurate are the results?
A: The results are accurate to 6 decimal places, which is sufficient for most practical applications in geometry and engineering.